References
[1]. Armstrong, B.E. & Larson, C.N. (1995). “Students' use of part-whole & direct comparison strategies for comparing
partitioned rectangles”. Journal of Research in Mathematics Education, Vol.26, No.1, pp.2-19.
[2]. Bezuk, N. S. & Bieck, M. (1993). “Current research on rational numbers and common fractions: Summary and
implications for teachers”. In D. Owens (Ed.), Research Ideas for the Classroom: Middle Grades Mathematics (pp.118-136).
New York: Macmillan Publishing Company.
[3]. Behr, M., Harel, G., Post, T. & Lesh, R. (1993). “Rational numbers: Toward a semantic analysis-emphasis on the operator
construct”. In T. P. Carpenter, E. Fennema & T. A. Romberg (Eds.), Rational Numbers: An Integration of Research, pp.13-47.
Hillsdale, NJ: Erlbaum.
[4]. Brown, G., & Quinn, R. J. (2006). “Algebra students' difficulty with fractions: An error analysis”. Australian Mathematics
Teacher, Vol.62, pp.28-40.
[5]. Brown, G.B., & Quinn, R.J. (2007). “Investigating the relationship between fraction proficiency and success in algebra”.
Australian Mathematics Teacher, Vol.63, pp.8-15.
[6]. Carpenter, T., Corbitt, M., Kepner, H., Lindquist, M., & Reys, R. (1980). “National assessment: A perspective of students'
mastery of basic mathematics skills”. In M. M. Lindquist (Ed.), Selected Issues in Mathematics Education (pp.215-227).
Chicago: National Society for the Study of Education and Reston, VA: National Council of Teachers of Mathematics.
[7]. Clarke, D.M., & Roche, A. (2009). “Students' fraction comparison strategies as a window into robust understanding and
possible pointers for instruction”. Educational Studies in Mathematics, Vol.72, pp.127-138.
[8]. Empson, S. & Levi, L. (2011). Extending Children's Mathematics: Fractions and Decimals: Innovations in Cognitively
Guided Instruction. Portsmouth, NH: Heinemann. pp.178-216.
[9]. Gould, P., Outhred, L. N., & Mitchelmore, M. C. (2006). “One-third is three-quarters of one-half”. In P. Grootenboer, R.
th Zevenbergen & M. Chinnappan (Eds.), Identities, Cultures and Learning Spaces (Proceedings of the 29 Annual
Conference of the Mathematics Education Research Group of Australasia, Vol.1, pp.262-269). Adelaide: MERGA..
[10]. Groff, P. (1996). “Is teaching fractions a waste of time?” Clearing House, Vol.69, pp.177-179.
[11]. Hasemann, K. (1981). “On difficulties with fractions”. Educational Studies in Mathematics, Vol.12, pp.71-87.
[12]. Hecht, S.A., Close, L., & Santisi, M. (2003). “Sources of individual differences in fraction skills”. Journal of Experimental
Child Psychology, Vol.86, No.4, pp.277-302.
[13]. Huinker, D. (1998). “Letting fraction algorithms emerge through problem solving”. In L. J. Morrow and M. J. Kenny (Eds.),
The Teaching and Learning of Algorithms in School Mathematics (pp.198-203). Reston, VA: National Council of Teachers of
Mathematics.
[14]. Huinker, DeAnn (2002). “Examining dimensions of fraction operation sense”. NCTM 2002 Yearbook: Making Sense of
Fractions, Ratios and Proportions, (pp.72-78).
[15]. Hiebert, J. (1988). “A theory of developing competence with written mathematical symbols”. Educational Studies in Mathematics, Vol.19, pp.333-355.
[16]. Jigyel, K., & Afamasaga-Fuata'i, K. (2007). “Students' conceptions of models of fractions and equivalence”. Australian
Mathematics Teacher, Vol.63, pp.17-25.
[17]. Kamii, C. & Clark, F.B. (1995). “Equivalent fractions: Their difficulty and educational implications”. Journal of
Mathematical Behavior, Vol.14, pp.365-378.
[18]. Kieren, T. (1995). “Creating spaces for learning fractions”. In J. T. Sowder & B.P. Schappelle (Eds.), Providing a Foundation
for Teaching Mathematics in the Middle Grades, (pp.31-65). New York: State University of New York Press.
[19]. Kilpatrick, J., Swafford, J., Findell, B., (2001). Adding it Up: Helping Children Learn Mathematics. The National
Academics Press, Washington, DC.
[20]. Kong, S. C. (2008). “The development of a cognitive tool for teaching and learning fractions in the mathematics
classroom: A design-based study”. Computers & Education, Vol.51, No.2, pp.886-899.
[21]. Lipkus, I. M., Samsa, G., & Rimer, B. K. (2001). “General Performance on a Numeracy Scale among Highly Educated
Samples”. Medical Decision Making, Vol.21, No.1, pp.37-44.
[22]. Mamolo, A., Sinclair, M., & Whiteley, W. J. (2011). “Proportional reasoning with a pyramid”. Mathematics Teaching in
the Middle School, Vol.16, No.9, pp.544-549.
[23]. Moss, J. & Case, R. (1999). “Developing children's understanding of the rational numbers: A new model and an
experimental curriculum”. Journal for Research in Mathematics Education, Vol.30, No.2, pp.122-147.
[24]. Niemi, D. (1996). “Instructional influences on content area explanations and representational knowledge: Evidence for
the construct validity of measures of principled understanding”. CSE Technical Report 403, Los Angeles: National Center for
Research on Evaluation, Standards, and Student Testing, University of California.
[25]. National Assessment of Educational Progress, (2005). The Nation's Report Card: Mathematics 2005. Retrieved from
http://nces.ed.gov/nationsreportcard/pdf/main2005/2006453.pdf
[26]. Orpwood, G., Schollen, L., Leek, G., Marinelli-Henriques, P., & Assiri, H. (2011). College Mathematics Project. Ministry of
Education and the Ontario Ministry of Training, Colleges and Universities. Toronto: Seneca College of Applied Arts and
Technology. Retrieved from http://collegemathproject.senecac.on.ca/cmp/en/pdf/FinalReport/2011/CMP_2011_Final_
Report%20-%2002Apr12%20pmh.pdf
[27]. Petit, M., Laird, R., & Marsden, E. (2010). A Focus on Fractions. New York, NY: Routledge.
[28]. Pitkethly, A., & Hunting, R. (1996). “A review of recent research in the area of initial fraction concepts”. Educational
Studies in Mathematics, Vol.30, pp.5-38. Retrieved from http://dx.doi.org/10.1007/BF00163751
[29]. Reyna, V. F., & Brainerd, C. J. (2008). “Numeracy, risk communication, and medical decision making”. Learning and
Individual Differences, Vol.17, pp.147-159.
